Streamline curvature and bed resistance in shallow water flow

The relationship between streamline curvature and bed resistance in shallow water flow with little side constraint, as derived in 1970 by H.J. Schoemaker, is reconsidered. Schoemaker concluded that the bed resistance causes the curvature of a free streamline to grow exponentially with the distance along this streamline, thus giving rise to a destabilizing tendency. The present analysis shows the bed shear stress to act in a stabilizing way and, as far as it is possible to isolate the influence of the bed resistance on the development of streamline curvature, it is shown to be a damping one. In addition, the applicability of the shallow water equations to the sealing of curved alluvial river models is discussed. It is suggested to introduce additional terms into the streamwise momentum equation, accounting for the advective influence of the secondary flow.Hydraulic EngineeringCivil Engineering and Geoscience